Quantitative uniqueness for the power of the Laplacian with singular coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, p. 513-529

In this paper we study the local behavior of a solution to the l-th power of the Laplacian with singular coefficients in lower order terms. We obtain a bound on the vanishing order of the nontrivial solution. Our proofs use Carleman estimates with carefully chosen weights. We will derive appropriate three-sphere inequalities and apply them to obtain doubling inequalities and the maximal vanishing order.

Published online : 2018-06-21
Classification:  35J15,  35A02
@article{ASNSP_2011_5_10_3_513_0,
     author = {Lin, Ching-Lung and Nagayasu, Sei and Wang, Jenn-Nan},
     title = {Quantitative uniqueness for the power of the Laplacian with singular coefficients},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {3},
     year = {2011},
     pages = {513-529},
     zbl = {1237.35164},
     mrnumber = {2905377},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_513_0}
}
Lin, Ching-Lung; Nagayasu, Sei; Wang, Jenn-Nan. Quantitative uniqueness for the power of the Laplacian with singular coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 513-529. http://www.numdam.org/item/ASNSP_2011_5_10_3_513_0/

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